$q$-差分算子 $L_q^{2}( 0, + \infty )$

IF 0.7 Q2 MATHEMATICS Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics Pub Date : 2023-03-30 DOI:10.31801/cfsuasmas.1121701

M. Sertbaş, Coşkun Saral

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摘要

在Hilbert空间$L_q^｛2｝（0，+\infty）$中，给出了由$q$差分表达式定义的极小算子和极大算子。讨论了极小算子的$q^{-1}$正规扩张的存在性问题。此外，还检验了最小算子谱和最大算子谱的集合。

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$q$-Difference Operator on $L_q^{2}( 0, + \infty )$

In this research, the minimal and maximal operators defined by $q$- difference expression are given in the Hilbert space $L_q^{2}( 0, + \infty )$. The existence problem of a $q^{-1}$-normal extension for the minimal operator is mentioned. In addition, the sets of the minimal operator spectrum and the maximal operator spectrum are examined.

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Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics MATHEMATICS-

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